Tumbling in nematic polymers and liquid crystals

Abstract: Most, but not all, liquid crystals tend to align when subject to shear flow, while most nematic polymeric liquid crystals undergo a tumbling instability, where the director rotate with the flow. The reasons of this instability remain elusive, as it is possible to find similar molecules exhibiting opposite behaviors. We propose a theory suitable for describing a wide range of material behaviors, ranging form nematic elastomers to nematic polymers and nematic liquid crystals, where the physical origins of tumbling emerge clearly. There are two possible ways to relax the internal stress in a nematic material. The first is the reorganization of the polymer network, the second is the alignment of the network natural axis with respect to the principal direction of the effective strain. Tumbling occurs whenever the second mechanism is less efficient than the first and this is measured by a single material parameter $\xi$. Furthermore, we provide a justification of the experimental fact that at high temperatures, in an isotropic phase, only flow alignment is observed and no tumbling is possible, even in polymers.